In traditional phase modulation, a data signal .phi.(t) is impressed on a carrier wave of frequency f.sub.c to produce a modulated signal EQU cos (2.pi.f.sub.c t+.phi.(t)),
where .phi.(t) is a baseband data signal of bit period .tau.. .phi.(t) in turn carries the data differentially encoded in which, for example, a phase change in .phi.(t) represents a logic 1 and no phase change represents a logic 0. In binary phase modulation, for example, .phi.(t) has two values, 0 and .tau..
In the conventional method of differential demodulation, a delay of .tau. is used to demodulate the modulated signal. Generally, the quadrature data signal EQU sin (2.pi.f.sub.c t+.phi.(t))
is produced so that an arctangent (tan.sup.-1) operation can be performed. The production and use of corresponding sine and cosine signals in radio frequency receivers is well known in the prior art. This is generally accomplished by injecting both the sine and cosine of an intermediate frequency (IF) into a pair of IF stages at the last stage of an IF down-conversion chain.
As illustrated in FIG. 1, the arctangent operation 12 yields the argument of the sine and cosine functions. The argument is applied to a delay line 14, the output of which is obtained with the argument at a summing junction 16. This operation yields the term EQU 2.pi.f.sub.c t-2.pi.f.sub.c (t-.tau.)+.phi.(t)-.phi.(t-.tau.)
as shown in FIG. 1. Because the desired data signal is EQU cos (.phi.(t)-.phi.(t-.tau.)),
it would be convenient if the term EQU 2.pi.f.sub.c t-2.pi.f.sub.c (t-.tau.)=2.pi.f.sub.c .tau.
contributed nothing to the result output by cosine operator 18. This term can be rewritten as EQU 2.pi.f.sub.c /f.sub.d, where f.sub.d =1/.tau. is the data frequency.
If the carrier frequency is chosen as f.sub.c =nf.sub.d, where n is a positive integer, the output of the cosine operator 18 of FIG. 1, EQU cos (2.pi.f.sub.c t-2.pi.f.sub.c (t-.tau.)+.phi.(t)-.phi.(t-.tau.)),
becomes EQU cos (2.pi.f.sub.c .tau.+.phi.(t)-.phi.(t-.tau.))=cos (.phi.(t)-.phi.(t-.tau.))
because EQU 2.pi.f.sub.c .tau.=2.pi.f.sub.c /f.sub.d,
which simplifies to EQU 2.pi.n, when f.sub.c =nf.sub.d.
The exact result of the foregoing operations depends on the amount of phase modulation. In binary differentially encoded modulation, for example, if zero angle represents 0 and .pi. represents a 1, then no phase change (0 to 0 or .pi. to .pi.) yields 0 and phase changes .pi. to 0 and 0 to .pi. yield .pi. and -.pi., respectively. As indicated in FIG. 1, cosine operator 18 is used to output cos (0)=1, or cos (.pi. or -.pi.)=-1. In this example, +1 can represent logic 1 and -1 can represent logic 0.
A limitation of prior art demodulators is that if, for some reason, f.sub.c is not, or cannot be chosen to be, equal to nf.sub.d, then the demodulation fails. For example, if the carrier frequency f.sub.c =(n+1/2)f.sub.d, then an angle of .pi. is introduced and the data are simply reversed. This result is satisfactory if it is planned. However, if f.sub.c =(n+1/4)f.sub.d, then an angle of .pi./2 is introduced and the data are lost, because cos (2n.pi.+.pi./2)=0.
For baseband systems, f.sub.c can be chosen carefully and held precisely, at least in practical terms. In RF systems, f.sub.c is the original RF carrier frequency that is converted down through a series of IF stages. As explained above, the total of the resulting f.sub.c uncertainty must be held to a fraction of f.sub.d /4. This is generally not a problem at HF with relatively high data rates, for example. However, f.sub.c cannot always be chosen with sufficient precision in some data transmission systems.
In mobile satellite communication systems, for example, where L-band carriers in the vicinity of 10.sup.9 Hz are used with low data rates, Doppler shift alone exceeds 100 Hz even for relatively slow moving land vehicles, yet the available power may only support data rates of 50 to 100 Hz. In this type of system, f.sub.c errors pose a significant problem. Thus, there is a need for a method of demodulation that can extract the data signals independent of the carrier frequency so that data is not lost as a result of carrier frequency shifts and uncertainty.